An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1\, kg$ moves with a speed of $12 \,m s^{-1}$ and the second part of mass $2\, kg$ moves with $8 \,m s^{-1}$ speed. If the third part files off with $4 \,m s^{-1}$ speed, then its mass is ......... $kg$
$7 $
$17 $
$3$
$5$
Explain the conservation of linear momentum for the radioactive decay of radium nucleus.
$A$ parallel beam of particles of mass $m$ moving with velocity $v$ impinges on $a$ wall at an angle $\theta$ to its normal . The number of particles per unit volume in the beam is $n$ . If the collision of particles with the wall is elastic, then the pressure exerted by this beam on the wall is :
A cannon ball is fired with a velocity $200\, m/sec$ at an angle of $60^o$ with the horizontal. At the highest point of its flight it explodes into $3$ equal fragments, one going vertically upwards with a velocity $100\, m/sec$, the second one falling vertically downwards with a velocity $100\, m/sec$. The third fragment will be moving with a velocity
A $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m / s$ and $Q$ with speed $40 \,m / s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about
A cart loaded with sand moving with velocity $v$. Sand is falling through the hole as shown in diagram then after falling on the ground sand is